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Relatively Free Semigroups of Intermediate Growth

2001
*
Journal of Algebra
*

*One*

*of*

*the*main purposes

*of*this paper is to give examples

*of*

*relatively*Ž .

*free*

*semigroups*and monoids having intermediate growth Section 6 . ... Quite recently our methods helped us to construct examples

*of*

*relatively*

*free*

*semigroups*

*of*Ž . intermediate growth and maximal equals 1 Gelfand᎐Kirillov

*superdimension*. ...

*The*equality 160 shows that induces a

*one*-to-

*one*correspondence Ä 4 between

*the*set

*of*all finite sequences ␣ as above and

*the*set

*of*all n words

*of*

*the*type ⌬ U over

*the*alphabet ⌽. ...

##
###
Page 2861 of Mathematical Reviews Vol. , Issue 97E
[page]

1997
*
Mathematical Reviews
*

Mat. 54 (1990), no. 5, 899-927; MR 92h:16020]

*the*author presents*the*following broad result: if T is*the**semigroup**of*automorphisms*of*a*free*countably generated algebra over a field*of*characteristic ... 0, and R is a*relatively**free*algebra satisfying a standard identity, then R is Noetherian as an F[7]-module. ...##
###
Growth, unavoidable words, and M. Sapir's conjecture for semigroup varieties

2004
*
Journal of Algebra
*

Some applications including examples

doi:10.1016/j.jalgebra.2003.09.021
fatcat:ggdkpnq4cna3begbds2tc24vdi
*of*f.g.*relatively**free**semigroups*having intermediate growth and maximal (equals 1)*superdimension*are considered. 483 Let U be a word over*the*alphabet Λ and W a ... Furthermore,*the*length*of**the*period is bounded above by a constant which depends only*on**the*number n and*on**the*number*of*generators*of*S. ... We also find*the*first example*of*a*relatively**free*f.g.*semigroup*which has intermediate growth and*superdimension*1 (Theorem 4.1) and a similar example*of*a*semigroup*which is*nilpotent*in*the*sense ...##
###
On generating functions for subalgebras of free Lie superalgebras

2002
*
Discrete Mathematics
*

But

doi:10.1016/s0012-365x(01)00262-x
fatcat:ewc4vask4nekxjwqg4fzjoj42i
*the*appropriate formula exists in terms*of*formal power series.*The*result is obtained in generality*of**free*Lie superalgebras, graded by some*semigroups*. ... In this case instead*of*formal power series we use elements*of**the*completion*of*a*semigroup*ring, which are called characters. ... In particular, this is*the*case, if A is a*relatively**free*superalgebra*of*some variety with*the*generating set X = X + ∪ X − . ...##
###
Monomial algebras

1997
*
Journal of Mathematical Sciences
*

*relatively*

*free*) algebras. ... A.A.Kirillov and M.L.Koncevich [26] constructed a

*relatively*

*free*Lie algebra

*of*an intermediate growth:

*the*Lie algebra

*of*generic vector elds

*on*a variety. ...

*The*method

*of*generalization uses

*the*passage to an associative algebra

*of*(left) ...

##
###
From minimal geodesics to supersymmetric field theories
[chapter]

2010
*
CRM Proceedings and Lecture notes AMS
*

For example,

doi:10.1090/crmp/050/20
fatcat:s3kjzsqnznaupldmukl7y6phym
*the*maximal number*of*independent vector fields*on**the*n-sphere was determined explicitly. ... From these classical descriptions we move via spaces*of*unbounded operators and super-*semigroups**of*operators to our most recent model, which is given by certain spaces*of*supersymmetric (1|1)-dimensional ... referred to as*the**superdimension*. ...##
###
Schild Action
[chapter]

2004
*
Concise Encyclopedia of Supersymmetry
*

*Semigroup*congruences are important for

*the*study and classification

*of*complex physical phenomena, especially when applied to

*free*

*semigroups*and monoids. Bibliography [1] A. H. Clifford and G. B. ... T from

*the*set

*of*elements

*of*

*semigroup*S into

*the*set

*of*elements

*of*

*semigroup*T such that /ðxyÞ ¼ /ðxÞ/ðyÞ for all x; y 2 S. When / is bijective, then S and T are isomorphic

*semigroups*. ... A simple example is

*the*following

*one*for a

*free*model

*of*where Q BRS ic a k a ; @t . This is an N ¼ 2 supersymmetry. ...

##
###
A Cyclic Orbifold Theory for Holomorphic Vertex Operator Algebras and Applications
[article]

2017
*
arXiv
*
pre-print

We use these results to construct five new holomorphic vertex operator algebras

arXiv:1611.09843v2
fatcat:ni2mohubjje67gcix7t5dtfeyq
*of*central charge 24 as lattice orbifolds, contributing to*the*classification*of**the*V_1-structures*of*suitably regular, ... To this end we describe*the*fusion algebra*of**the*fixed-point vertex operator subalgebra V^G and show that V^G has group-like fusion. ... I enjoyed working together with both*of*them*on**the*paper [EMS15] , which is partly based*on*this dissertation and vice versa. ...